In this paper, we investigate unconstrained and constrained sample-based federated optimization, respectively. For each problem, we propose a privacy preserving algorithm using stochastic successive convex approximation (SSCA) techniques, and show that it can converge to a Karush-Kuhn-Tucker (KKT) point. To the best of our knowledge, SSCA has not been used for solving federated optimization, and federated optimization with nonconvex constraints has not been investigated. Next, we customize the two proposed SSCA-based algorithms to two application examples, and provide closed-form solutions for the respective approximate convex problems at each iteration of SSCA. Finally, numerical experiments demonstrate inherent advantages of the proposed algorithms in terms of convergence speed, communication cost and model specification.